'Signature archiving' is generally understood as converting the signature to a form in which it does not need external information sources for validation.
In other words, an archived signature contains all the information needed to establish its validity without contacting CAs and their representatives (CRLs, OCSP responders, certificate directories).
Often such signatures are additionally certified by a trusted third party by the means of the special, archival, timestamps, made over the entire signature content.

The low-level signature archiving assumes that you have (or can obtain) the following information:

The whole certificate chain for the signing certificate;

OCSP responses and CRLs for all certificates where assumed;

Whole certificate chains for every timestamp and the OCSP certificate involved

OCSP responses and CRLs for all such certificates.

To archive the signature, obtain a signature object (TElCMSSignature) first.
It can be either a brand new CMS message and its signature, or an already existing signed message loaded into a TElSignedCMSMessage object.